Problem: Rewrite as a simplified fraction. ${0.84\overline{6} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 846.6666...\\ 100x &= 84.6666...\end{align*}}$ Subtracting the two equations, we have: ${900x = 762}$ ${x = \dfrac{762}{900}} $ ${x = \dfrac{127}{150}} $